| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 75 | |
| Number of page(s) | 35 | |
| DOI | https://doi.org/10.1051/cocv/2021068 | |
| Published online | 13 July 2021 | |
Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions*
1
Department of Mathematics and Statistics, Faculty of Science, Masaryk University,
Kotlářská 2,
61137
Brno, Czech Republic.
2
Department of Mathematics, Michigan State University,
East Lansing,
MI
48824-1027, USA.
** Corresponding author: hilscher@math.muni.cz
Received:
31
July
2020
Accepted:
22
June
2021
In this paper we develop a new approach for optimal control problems with general jointly varying state endpoints (also called coupled endpoints). We present a new transformation of a nonlinear optimal control problem with jointly varying state endpoints and pointwise equality control constraints into an equivalent optimal control problem of the same type but with separately varying state endpoints in double dimension. Our new transformation preserves among other properties the controllability (normality) of the considered optimal control problems. At the same time it is well suited even for the calculus of variations problems with joint state endpoints, as well as for optimal control problems with free initial and/or final time. This work is motivated by the results on the second order Sturm–Liouville eigenvalue problems with joint endpoints by Dwyer and Zettl (1994) and by the sensitivity result for nonlinear optimal control problems with separated state endpoints by the authors (2018).
Mathematics Subject Classification: 49K15 / 49K40 / 90C31
Key words: Optimal control problem / joint (coupled) endpoints / separated endpoints / controllability / strong Pontryagin principle / coercivity / sensitivity analysis / free time problem
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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